Histograms

Every process has variation and often displays some pattern. A histogram is one of the basic quality tools used to analyze variation in a set of data. It helps you understand how the data collected from a particular development or production process is distributed in terms of frequency of occurrences of a particular value in the set. The key objective is to look for stability and predictability.

A histogram provides a quick look at how the process data is distributed. So-called normally distributed histograms, also called Gaussian histograms, are bell-shaped and display distinct statistical properties. Such unimodal curves are associated with stable processes that are predictable in their variation. Such variation around the bell shape is called chance or natural variation. The variations that are not characterized by a bell shape may be due to various process defects that can be attributed to special and identifiable causes, and may be associated with unstable processes. However, several "exotic" distributions, such as exponential, gamma, beta, Weibull, binomial, and Poisson, are not bell-shaped but are associated with stable and predictable processes. These and other distributions are well-known and statistically characterizable.

An inspection of histograms can provide clues to problems in the process, data sampling, or data collection methodology. It reveals possible problem areas that may be difficult to figure out from mere tabulation of data. The following sections briefly cover various uses of histograms in data analysis, as described by Ozeki, Asaka, and Kume.^[6], ^[7]

Determining the Distribution Pattern

A normal distribution indicates a stable process and data integrity. Within normal distributions, histograms reveal variability differences between two plots (see Figure 6.9). "Double peak" (see Figure 6.10) and "isolated island" indicate mixing of data. A steep "cliff" may be due to including items that do not meet specifications.

Figure 6.9. Examples of Histograms with Normal Distributions but Different Variabilities

Figure 6.10. An Example of a Histogram with Double Peak

Determining Whether Specifications Are Satisfied

A normal distribution in which the center is equidistant from specified limits with room to spare represents a stable system that is easy to maintain. Distributions with centers closer to one or the other limit, and distributions outside the limits, may require corrective measures to bring the mean closer to the center and the need to reduce variation.

Comparing Data by Stratifying

To find the causes of defects, it is useful to divide the data into groups (stratas) by equipment used, shift worked, procedure deployed, or developers involved. The method of grouping by common characteristics is called stratification. By comparing the groups, it may be possible to discover the causes and structure of variability.